Automated interfacial tensiometer

ABSTRACT

The interfacial tension in a liquid-liquid system is determined by estimating the flow rate of the heavier liquid as it is discharged under constant head through a capillary immersed in a body of the lighter liquid, or conversely, of the lighter liquid as it is discharged under constant head through a capillary immersed in a body of the heavier liquid. A known voltage is applied to each drop which forms at and detaches from the capillary tip and an electrometer is used to measure the total electrical charge per drop and the frequency of drop formation/detachment. The determination is made under conditions in which a plot of interfacial tension versus the square of the applied voltages yields two straight lines whose slopes of ±C/2 where C is the capacitance of the interface per unit area and the positive value is generated from the positive polarity voltage and the negative from the negative polarity. Based upon the value of C determined from the slope, the known voltage and the measured values of dropping frequency and of total charge per drop, the correctness of the estimated flow rate is determined and, in an iterative process, a new flow rate estimation and consequent plots are made until the estimated flow rate equals the flow rate as determined from measurements. The value of the interfacial tension at zero charge is then obtained from the intersection of the two lines.

This application is a continuation-in-part of prior filed copendingapplication Ser. No. 606,289, now U.S. Pat. No. 4,569,226 filed May 2,1984, for an Automated Interfacial Tensiometer.

BACKGROUND OF THE INVENTION

There are a number of techniques for the purpose of determininginterfacial tension in a liquid-liquid system. The Jobe Pat. No.3,913,385 and corresponding published patent application No. B 351,735employ a continuous type monitor for hydrocarbon liquids forautomatically detecting the presence of a surface active agent in thehydrocarbon liquid, and employ a caustic liquid to form drops in themonitored liquid. The Davis U.S. Pat. No. 4,196,615 employs atensiometer which measures changes in capacitance between monitoredplates as effected by passage of drops of one liquid falling through abody of a second liquid. The Jobe U.S. Pat. No. 3,881,344 measuressurface tension of a stream of flowing liquid as a function of thepressure required to form an air bubble below the surface of the liquid.The Jennings, Jr. et al. U.S. Pat. No. 3,483,737 employs apparatus formeasuring interfacial tension by the pendant drop method. The Russianreference SU-601-602 (Sakalskii) employs an instrument in which highvoltage is used to break up the surface of a liquid, the voltage valueat that time being a measure of the surface tension.

Many methods involve withdrawing a sample, preparing for analysis andthen making measurement of interfacial tension according to:

(a) pendant drop method--in which one liquid is allowed to grow slowlyfrom a capillary immersed in a second liquid. Either the detached dropis weighed or a photograph is made and an analysis is performed on theshape.

(b) ring method--a ring is immersed to the level of the interface andthe ring is slowly pulled out of the interfacial region and the forcemeasured.

(c) spinning drop method--a drop of the lighter liquid is placed in acapillary between columns of the heavier liquid and rotated about theaxis; and analysis of the contact angle is made.

BRIEF SUMMARY OF THE INVENTION

In many industrial processes it is desirable to be able to measureinterfacial tension between two liquids or between two liquids with asurface active agent adsorbed at the interface. The present invention isdirected to novel apparatus and method of measuring interfacial tensionin a liquid-liquid system and in particular to a technique which lendsitself to providing an automated, on-line tensiometer capable ofmeasuring and recording or otherwise reporting interfacial tensionbefore material is introduced into a process. Quality control or othertypes of monitoring functions are obviously possible. The technique hasthe capability of:

(a) instantaneous response;

(b) on-line measurement;

(c) direct read-out of interfacial tension;

(d) detection of trace amounts of surfactants;

According to the invention, a constant head is applied to a heavierliquid as it is discharged through the tip of a capillary immersed in abody of the lighter liquid. A pool of the heavier liquid is formedwithin the body of lighter liquid in spaced relation below the capillarytip and a known but variable d.c. voltage is maintained between theheavier liquid drop and this pool. According to an alternate embodimentof the invention, a constant head is applied to a lighter liquid as itis discharged through the tip of a capillary immersed in a body of theheavier liquid. A pool of the lighter liquid is formed above the body ofheavier liquid in spaced relation above the capillary tip and a knownbut variable d.c. voltage is maintained between the lighter liquid dropand this pool. Under these circumstances, the interfacial tension γbetween the liquids is related to the electrical charge Q per area of adrop and the applied voltage V according to the following:

    γ=γ.sub.o -1/2QV                               (1)

where γ_(o) is the interfacial tension in the absence of electricalcharge and is, hence, the value of interest.

If C, the capacitance of the interface per unit area, is constant over arange of voltages V, then Q=CV and equation (1) may be expressed as:

    γ=γ.sub.o -1/2CV.sup.2                         ( 2)

Since equation (2) is of the classical straight line form y=mx+b wherey=γ, x=V², m is the slope equal to C/2 and b is γ_(o) it demonstratesthat if γ is plotted versus V², such a plot will be a straight linewhich intercepts the ordinate at b, the value of γ equal to γ_(o).

However, the values of γ and C are both unknown and the desired plotcannot be made on the basis of equation (2).

The relation between interfacial tension, γ_(o), and liquid flow rate,q, has been developed by Scheele and Meister* for droplet formation atlow flow rates. These authors present a force balance on the suspendeddroplet wherein the terms ##EQU1## represents the gravitational force,interfacial tension, Stokes' drag, momentum, and volume added duringnecking.

The Stokes' drag term is negligible in these types of measurements, sothe above equation may be rearranged in more explicit form forinterfacial tension

    γ+Eγ1/3-F/f-G=0                                (3)

where E, F and G are constants and f is the frequency of dropformation/detachment, ##EQU2## where g=gravitational acceleration

ρp=density of heavier fluid

Δp=difference in density between heavier and lighter fluids

^(d) ori=inner orifice diameter of capillary

^(d) oro=outer orifice diameter of capillary ##EQU3##

A plot of γ versus V² based upon equation (3) will yield an accuratedetermination of γ_(o) to the extent that an accurate approximation of qhas been made and f has been accurately measured. The question, then isto check the accuracy of the estimated value of q and, if incorrect, toadjust it and repeat the plot according to equation (3) and check thenew estimated value of q until the correct value of q is found. At thattime, the ordinate intercept of the plot yields the correct value ofγ_(o). However, it is preferred for accuracy to make two plots fromequation (3), one in which V² vs. γ is generated from a positivepolarity and has a positive slope, and the other in which V² vs γ isgenerated from a negative polarity and has a negative slope. Thisgenerates two straight lines which intersect as γ_(o), which may notnecessarily occur at V² =0.

In order to check the estimated value of q, the slope of the plot isdetermined which, from equation (2), equals 1/2C. This value of C isused in equation (6) here following to check the accuracy of theestimation of q.

The volume Vol of an individual drop is: ##EQU4## where S is the surfacearea per drop. Since, by definition, the total charge Q_(T) per dropequals Q_(S), and since Q=CV, equation (4) may be expressed: ##EQU5##

Since the actual flow rate equals fVol, the estimated flow rate used inequation (3) can be checked for accuracy from measured values of V,f andQ_(T) and the value of C determined from the slope of equation (2).Thus, using the symbol q' to distinguish from the estimated flow rate qand using equation (5): ##EQU6##

Thus, if f and Q_(T) are measured and the value of C determined from theslope of the equation (2) plot, the accuracy of the estimated value of qmay be checked.

The values of V,Q_(T) and f may be measured by suitable electronicapparatus and if the solution of equation (6) indicates that theestimated value of q used in equation was in error, i.e., q≠q', a newvalue of q is used to form a new plot. This iterative process yieldsresults which display an accuracy of at least 0.60% in the measurementof interfacial tension.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

FIG. 1 is a schematic representation of one form of the invention;

FIG. 2 illustrates curves for the water-n-octane system with and withouta surfactant added;

FIG. 3 is a curve generated by successive dilutions to determine thepresence and amount of surfactant; and

FIG. 4 is a schematic representation of an alternate form of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a simplified diagram of a system according to the invention.The vessel or cell 1 is provided with an inlet line 2 for the heavierliquid supplied from any suitable constant head source and, within thevessel, the heavier liquid is discharged through the capillary 3 into abody 4 of the lighter liquid. The lighter liquid is introduced into thevessel through the inlet line 5 and is drained through the outlet line6. The line 5 is connected to any suitable constant head source for thelighter liquid and the body 4 is maintained at the fixed height withinthe vessel as is indicated by the reference character 7. Likewise, theheavier liquid is drained at the outlet line 8 so that, as supplied bythe constant head source of heavier liquid through the capillary 3, apool 9 of the heavier liquid is maintained whose interface 10 with thebody 4 of lighter liquid is maintained at a fixed level well below thetip of the capillary 3, i.e., large enough that the flow rate of theheavier liquid is unaffected by the electrical charge imparted to thedrops 11 of the heavier liquid.

The capillary 3 is metallic and is connected to the voltage source 12 bythe conductor 13 which is also connected as at 14 to suitableinstrumentalities for recordation and calculation. The voltage source isvariable and capable of delivering between 0 and 2000 volts of eitherpolarity. The pool 9 of the heavier liquid is grounded through theconductor 15 and the electrometer 16 to the ground connection 17 and theoutput conductor 18 of the electrometer is connected to theinstrumentalities for recordation and calculation. The electrometer iscapable of registering the frequency f of charge pulses generated by thedroplets striking the pool of heavier liquid. It is also capable ofmeasuring the flow of current delivered over a certain time andintegrating this quantity to obtain ##EQU7##

As noted earlier, the flow rate of the heavier liquid is unaffected bythe voltage supplied by the source 12 but the size of the drops 11 whichform at and detach from the capillary is affected. Thus, the size of thedrops and the frequency of drop formation/detachment is a function ofthe voltage. The electrometer 16 is used to measure the frequency f andthe total charge Q_(T) per drop for various values of V as measured fromthe voltage source 12. The estimated value q, the voltage V and themeasured frequency f are used to calculate the values of the γ vs V₂plots according to equation (3). At the same time, the values of f andQ_(T) and corresponding levels of voltage V are employed to calculatethe value of q' from equation (6). Typical γ vs V² plots are shown inFIG. 2, from which the slope C/2 is determined for use in equation (6)to complete the determination of q'. As noted before, an iterativeprocess is used until q=q', at which time the desired value γ_(o) isdetermined. FIG. 2 shows data for the water-n-octane system, and alsofor that same system with a surfactant, sodium dodecyl sulfate, added.Results of ten different concentrations of surfactant are presented inTable I. These results show that for the pure system, withoutsurfactant, the intersection of the two lines yields a value of 50.8dynes cm⁻¹, with a correlation coefficient of 0.991 for the positivepolarity and 0.999 for the negative polarity. The accepted value for theinterfacial tension at 20° C. is 50.8 dynes cm⁻¹. The interfacialcapacitance, obtained from the slopes of the γ vs V² curves, and theinterfacial tensions obtained from the intersections of the lines, forten different concentrations show that the capacitance is independent ofthe surfactant concentration and only slightly greater (1.088 vs 1.078statfarads cm⁻²) for the negative polarity when compared with thepositive.

                  TABLE I                                                         ______________________________________                                        CHARACTERISTICS OF INTERFACIAL TENSION VS                                     VOLTAGE.sup.2 PLOT AT SEVERAL SURFACTANT                                      CONCENTRATIONS                                                                          Interfacial  Interfacial                                                      Tension      Capacitance Correlation                                Concentration                                                                           at Zero      Statfarads cm.sup.- 2                                                                     Coefficient                                SDS       Charge       Polarity    Polarity                                   Moles l.sup.- 1                                                                         γo, dynes cm-.sup.- 1                                                                (+)     (-)   (+)  (-)                                 ______________________________________                                        0.00      50.8         1.084   1.128 0.991                                                                              0.999                               2.50 × 10.sup.-4                                                                  44.6         1.034   1.124 0.974                                                                              0.989                               5.00 × 10.sup.-4                                                                  40.2         1.122   1.094 0.994                                                                              0.998                               1.00 × 10.sup.-3                                                                  33.7         1.162   1.150 0.983                                                                              0.998                               3.00 × 10.sup.-3                                                                  22.4         1.372   1.118 0.993                                                                              0.993                               4.00 × 10.sup.-3                                                                  17.5         1.166   1.040 0.950                                                                              0.997                               6.25 × 10.sup.-3                                                                  8.85         1.082   1.112 0.993                                                                              0.983                               1.25 × 10.sup.-2                                                                  6.72         0.884   1.010 0.994                                                                              0.982                               2.50 × 10.sup.-2                                                                  6.30         0.848   0.938 0.998                                                                              0.980                               5.00 × 10.sup.-2                                                                  6.71         1.028   1.166 0.991                                                                              0.993                                                --C.sub.+  = 1.078  --C.sub.-  = 1.088                                        σ.sub.n.spsb.+  = 0.14 σ.sub.n.spsb.-  =                          0.0672                                                       ______________________________________                                    

FIG. 3 is a plot of the values of γ_(o) at the various surfactantconcentrations vs the log of the surfactant concentration C'. From theslope of this curve ##EQU8##

one is able to obtain Γ_(o) the amount of surfactant adsorbed at theinterface; k is Boltzmann's constant and T is temperature. This data ispresented in Table 2.

                  TABLE 2                                                         ______________________________________                                        ADSORPTION OF SODIUM DODECYL SULFATE                                          AT WATER-N--OCTANE INTERFACE                                                  Concentration                                                                           Interfacial -d.sub.γo                                                                         Adsorption                                    SDS       Tension     dlnC      at Interface                                  moles l.sup.- 1                                                                         γ.sub.o, dynes cm.sup.- 1                                                           dynes cm.sup.- 1                                                                        Γ.sub.o, molecules                      ______________________________________                                                                        nm.sup.2                                      0.00      50.8        0         0                                             2.50 × 10.sup.-4                                                                  44.6        1.97      0.479                                         5.00 × 10.sup.-4                                                                  40.2        6.14      1.49                                          1.00 × 10.sup.-3                                                                  33.7        9.86      2.40                                          3.00 × 10.sup.-3                                                                  22.4        9.86      2.40                                          4.00 × 10.sup.-3                                                                  17.48       20.0      4.86                                          6.25 × 10.sup.-3                                                                  8.85        20.0      4.86                                          1.25 × 10.sup.-2                                                                  6.72        3.26      0.792                                         2.50 × 10.sup.-2                                                                  6.30        0.782     0.190                                         5.00 × 10.sup.-2                                                                  6.71        -0.826    -0.201                                        ______________________________________                                    

This information is obtained from the invention by making a measurementof γ_(o) at the concentration of the unknown surfactant in the system.Then by making successive dilutions of the unknown surfactant in thesystem by successively diluting the system by additions of constantamounts of the pure liquid of the system, and measuring γ_(o) at eachdilution, one is able to generate a curve similar to that of FIG. 3. IfC₁ ' is the original unknown concentration of surfactant and the liquidcontaining this unknown concentration is mixed with an equal amount ofpure liquid to yield a new system of diluted concentration C₂ ', then##EQU9##

Now if γ_(o) is measured at these two concentrations C₁ ' and C₂ ':##EQU10##

The dilution factor 1/2 is used here as an example only, and in actualcases the dilution could be on the order of 0.8-0.9.

The presence and amount of surface active agent is then easilydetermined.

The invention has a number of advantages:

(a) The response at each voltage is almost instantaneous. Therefore, anelectronic instrument can scan the voltages, measure the correspondingfrequencies and determine the intersection of the two polarity lines ina few seconds.

(b) Liquids can be continuously fed into and out of the cell or vesselso that on-line measurements may be made.

(c) Direct read-out of interfacial tension is obtained.

(d) Even trace amounts of impurities which are surface active arerapidly detected.

An alternate embodiment of the present invention is shown in FIG. 4.Here, the vessel or cell 51 is provided with an inlet line 52 for thelighter liquid supplied from any suitable constant head source and,within the vessel, the lighter liquid is discharged through thecapillary 53 into a body 54 of the heavier liquid. The heavier liquid isintroduced into the vessel through the inlet line 55 and is drainedthrough the outlet line 56. The line 55 is connected to any suitableconstant head source for the heavier liquid and the body 54 ismaintained at the fixed height within the vessel as is indicated by thereference character 60, well above the tip of the capillary 53, i.e.,large enough that the flow rate of the lighter liquid is unaffected bythe electrical charge imparted to the drops 61 of the lighter liquid.

Likewise, the lighter liquid is drained at the outlet line 58 so that,as supplied by the constant head source of lighter liquid through thecapillary 53, a pool 59 of the lighter liquid is maintained at a fixedlevel 57.

The capillary 53 is metallic and is connected to the voltage source 62by the conductor 63 which is also connected as at 64 to suitableinstrumentalities for recordation and calculation. The voltage source isvariable and capable of delivering between 0 and 2000 volts of eitherpolarity. The pool 59 of the lighter liquid is grounded through theconductor 65 and the electrometer 66 to the ground connection 67 and theoutput conductor 68 of the electrometer is connected to theinstrumentalities for recordation and calculation. The electrometer iscapable of registering the frequency f of charge pulses generated by thedroplets striking the pool of lighter liquid. It is also capable ofmeasuring the flow of current delivered over a certain time andintegrating this quantity to obtain ##EQU11##

As similarly noted ealier, the flow rate of the lighter liquid isunaffected by the voltage supplied by the source 62 but the size of thedrops 61 which form at and detach from the capillary is affected. Thus,the size of the drops and the frequency of drop formation/detachment area function of the voltage. The electrometer 66 is used to measure thefrequency f and the total charge Q_(T) per drop for various values of Vas measured from the voltage source 62. The estimated value q, thevoltage V and the measured frequency f are used to calculate the valuesof the γ vs V² plots according to equation (3). At the same time, thevalues of f and Q_(T) and corresponding levels of voltage are employedto calculate the value of q' from equation (6). Typical γ vs V² plotsare shown in FIG. 2, from which the slope C/2 is determined for use inequation (6) to complete the determination of q'. As noted before, aniterative process is used until q=q', at which time the desired valueγ_(o) is determined.

While an embodiment of an automated interfacial tensiometer and amodification thereof have been shown and described in detail herein,various other changes and modifications may be made without departingfrom the scope of the present invention.

I claim:
 1. The method of determining the interfacial tension in aliquid-liquid system in which one liquid has a greater density than theother, which comprises the steps of:(a) forming a body of said oneliquid which is of greater density; (b) introducing said other liquidwhich is of lesser density dropwise into said one liquid at a rate whichmay be estimated; (c) imparting a total electrical charge Q_(T) on eachdrop of said other liquid by the application of voltage V and varyingsuch voltage so that some drops carry charges which are different fromthe charges of other drops; (d) measuring the frequency f of the dropsand the total electrical charge Q_(T) carried by each drop; (e)determining the values of the interfacial tension γ for different V andmeasured f and plotting γ vs V² therefrom; (f) determining the value ofthe capacitance C per unit area per drop from the slope of the plot ofstep (e) and calculating the value of actual flow rate q' based upon thevalue of C, f, V and Q_(T) ; and (g) repeating steps (a) through (e)until the estimated liquid flow rate of step (b) equals q'.
 2. Themethod as defined in claim 1 wherein the heavier and lighter liquids arecontinuously introduced into and withdrawn from a common vessel.
 3. Themethod as defined in claim 2 wherein each liquid is introduced into thecommon vessel at a respective constant head.
 4. The method ofdetermining the interfacial tension in a liquid-liquid system in whichone liquid has a greater density than the other, which comprises thesteps of:(a) forming a body of either one of said liquids; (b)introducing the other of said liquids into said body, dropwise at a ratewhich may be estimated; (c) imparting a total electrical charge Q_(T) oneach of said drops by the application of voltage V and varying suchvoltage so that some drops carry charges which are different from thecharges of other drops; (d) measuring the frequency f of the drops andthe total electrical charge Q_(T) carried by each drop; (e) determiningthe values of the interfacial tension γ for different V and measured fand plotting γ vs V² therefrom; (f) determining the value of thecapacitance C per unit area per drop from the slope of the plot of step(e) and calculating the value of actual flow rate q' based upon thevalue of C, f, V and Q_(T) ; and (g) repeating steps (a) through (e)until the estimated liquid flow rate of step (b) equals q'.
 5. Themethod as defined in claim 4 in which said liquids are continuouslyintroduced into and withdrawn from a common vessel.
 6. The method asdefined in claim 5 in which each of said liquids is introduced into thecommon vessel at a respective constant head.